Nonlinear observer for vehicle velocity estimation

A nonlinear observer for estimation of lateral and longitudinal velocity of automotive vehicles is proposed, based on acceleration and yaw rate measurements in addition to wheel speed and steering angle measurements. Stability of the observer is proved in the form of input-to-state stability of the observer error dynamics, under an assumption on the friction model. This assumption is treated with some detail. The observers are validated on experimental data from cars. INTRODUCTION Automotive feedback control systems for vehicle handling and/or active safety usually depend on information of vehicle velocity, sometimes in the form of the vehicle body side slip angle. While concepts for direct measurement of velocity exist, they are generally considered too expensive for use in production cars. Hence, concepts for inferential estimation of vehicle velocity using other (cheaper) measurements are of considerable interest. The main goal of this work is to develop a nonlinear observer for estimation of vehicle velocity. To provide a theoretical foundation for its implementation, explicit stability conditions for convergence of the estimated states are analyzed. The observer is based on nonlinear models for taking the nonlinear dynamics (mainly due to highly nonlinear friction and Coriolis forces) into account, and to obtain simple designs with few tuning knobs (as opposed to Extended Kalman Filter (EKF) designs). Another significant advantage over EKF designs, is that real-time solution of the Riccati differential equations is avoided, such that the observer can be implemented more efficiently in a low-cost embedded computer unit. A non-linear friction model is used for better exploiting the measurements. An important parameter in many friction Also affiliated with NTNU, Department of Engineering Cybernetics, N-7491 Trondheim, Norway models, the maximal friction coefficient μH , is known to vary significantly with different road conditions. We will assume this parameter to be known, or estimated by other means. While simultaneous estimation of velocity and μH might be a feasible path, we argue that estimation of μH requires special attention depending on the application the observer is used for, since it will be only weakly observable for many (normal) driving conditions, requiring monitoring, resetting and other logic functions to be implemented (see e.g. [7]). Earlier work on observers for estimation of lateral velocity are mainly based on linear or quasi-linear techniques, e.g. [3, 19, 17, 2]. A nonlinear observer linearizing the observer error dynamics have been proposed in [9, 10]. The same type of observer, in addition to an observer based on forcing the dynamics of the nonlinear estimation error to the dynamics of a linear reference system, are investigated in [5]. The problem formulation there assumes that the longitudinal wheel forces are known, as the observer implemented in ESP also does [18]. In our work, we do not make this assumption, as such information is not always available. The Extended Kalman Filter (EKF) is used as a nonlinear observer for estimating vehicle velocity and tyre forces in [13, 14], thus without the explicit use of friction models. A similar, but simpler, approach is suggested in [2]. An EKF based on a tyre-road friction models that also included estimation of the adhesion coefficient and road inclination angle is suggested in [16]. In [1], the use of an EKF is considered, based on a nonlinear tyre-friction model, that also includes estimation of cornering stiffness. The strategy proposed in [11] combines dynamic and kinematic models of the vehicle with numerical bandlimited integration of the equations to provide a side-slip estimate. In [4] the side-slip angle is estimated along with yaw rate in an approach that has similarities with the one considered herein, but without yaw-rate measurements. The approach is validated using experimental data, but there are no stability proofs.